A 2-column table with 8 rows. The first column is labeled t with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 54, negative 20, negative 4, 0, negative 2, negative 4, 0, 16.
Using only the values given in the table for the function, f(x) = x3 – 3x – 2, what is the interval of x-values over which the function is decreasing?

Without looking at the answers we are going to deduce what intervals could make f(x) positive. Well, where is it shown as positive for the numbers given? well f(-1) and f(0) are positive, both at 2. then both f(-2) and f(1) are 0, then everything below -2 and above 1 make f(x) negative, so it looks like everything up until -2 is negative, but increasing then at -2 it turns to 0 and keeps increasing at least until some time after f(-1). It might even just stay at 2 until it gets to f(0), and then after that it decreases. Hopefully that makes sense.

Given the description, and if you on't understand I can try to explain more carefully, where does it look like it's positive? Well, it goes from negative to 0 at -2, then after that it's positive until 1, where it turns to 0 again, before decreasing. so everything between -2 and 1 look to make f(x) positive. Since f(-2) and f(1) don't themselves though it means they are not included, so you use parenthesis.

so the answer is (-2,1) Again, let me know if you need more of an explanation.